We propose a theoretical statistical analysis for systems of interacting diffusions, possibly with common noise and/or degenerate diffusion components, in a mean-field regime. These models are more or less widely used in finance, MFG, systemic risk analysis, behaviourial sociology or ecology. We consider several inference issues such as: i) nonparametric estimation of the solution of the underlying Fokker-Planck type equation or the drift of the system ii) testing for the interaction between components iii) estimation of the interaction range between particles.

This talk is based on joint results with C. Fonte and L. Della Maestra.

Underlying paper: https://arxiv.org/abs/2011.03762 (with L. Della Maestra)

Personal website of Marc Hoffmann

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